1. (AAC/ACA c9q1). For each of the following studies, decide whether you can reject the null hypothesis that the groups come from identical populations. Use the alpha = .05 level.1a.
|
|
Group 1
|
Group 2
|
Group 3
|
|
n
|
10
|
10
|
10
|
|
M
|
7.4
|
6.8
|
6.8
|
|
S2 (estimated variance)
|
.82
|
.90
|
.80
|
1b.
|
|
Group 1
|
Group 2
|
Group 3
|
Group 4
|
|
n
|
25
|
25
|
25
|
25
|
|
M
|
94
|
101
|
124
|
105
|
|
S (estimated standard deviation)
|
24
|
28
|
31
|
25
|
2.(AAC/ACA c9 q3). A psychologist at a private psychiatric hospital was asked to determine whether there was a difference in the length of stay of patients with different categories of diagnosis. Looking at the last four patients in each of the three major categories, the results (in weeks of stay) were as follows:
|
Diagnosis Category
|
|
Affective Disorders
|
Cognitive Disorders
|
Drug-Related Conditions
|
|
7
|
12
|
8
|
|
6
|
8
|
10
|
|
5
|
9
|
12
|
|
6
|
11
|
10
|
a. Write out the null hypothesis for this example.
b. Using alpha = .05, decide whether there is a difference in the length of stay among the different diagnosis categories. Give appropriate statistical evidence for your conclusion.
c. Determine the effect size
3. (AAC/ACA c9q23). An experiment is conducted in which 60 participants each fill out a personality test, but not according to the way they see themselves. Instead, 20 are randomly assigned to fill it out according to the way they think a parent sees them (i.e. how a parent would fill it out to describe the participant); 20 as their best friend would fill it out for them; and 20 as the professors they know best would fill it out for them. The main results appear in the table below. Explain these results to a person who has not taken a course in statistics.
Table 4.1 Means for Main Personality Scales for Each Experimental Condition.
|
Scale
|
Parent
|
Friend
|
Professor
|
F(2,57)
|
|
Conformity
|
22
|
12
|
16
|
5.08**
|
|
Extroversion
|
14
|
15
|
13
|
2.89
|
|
Maturity
|
15
|
22
|
19
|
4.12*
|
|
Self-confidence
|
40
|
27
|
32
|
3.58*
|
*p< .05, **p< .01
4. (AAC/ACA c9q24). Friend (2001), compared three methods of teaching writing. Students were randomly assigned to three different experimental conditions involving different methods of writing a summary. At the end of two days of instruction, participants wrote a summary. One of the ways it was scored was the percentage of specific details of information that it included from the original material Here is a selection from her article describing one of the findings:
a. Explain these results to a person who has never had a course in statistics.
b. Explain, to the same person, why this data was analyzed using an ANOVA, instead of 3 independent t tests.
c. Based on the information given, determine the effect size.